5, A 10-year loa n with an effective annual interest rate of 5% is to be repaid
ID: 2804836 • Letter: 5
Question
5, A 10-year loa n with an effective annual interest rate of 5% is to be repaid with the following payments 200 at end of year 2 4 6 600 800 1000 10. Calculate the amount of principal in the second payment. 199.64 193.64 185.64 181.64 171.64 6 What is the duration of a 4 year bond with 8% annual coupons and par value $1000 if the present interest rate is 4%? 3.21 3.31 3.41 3.51 3.61 athend of years 1 and 2, respectively. The only investments available are two Bonds. Bond 1 matures in 1 year and yields 10%. Bond 2 matures his liabilities exactly. 2, respectively. The only investments available are two zero-coupon 2d yields 10%. Bond 2 matures in 2 years and has a yield rate of 12%. Determine your cost to match 2756 2259 2007Explanation / Answer
5. First calculate the present value of loan by discount the amount paid at 5%
Year (t)
Amount (A)
PV = (A/(1+5%)^t
2
$200
$181.41
4
$400
$329.08
6
$600
$447.73
8
$800
$541.47
10
$1,000
$613.91
Total Loan (sum of Pvs)
$2,113.60
Now we know that loan amount is $2,113.60 and paying 5% interest per year at 2 years interval
Year (t)
Beginning balance (BB)
Loan with two years interest @ 5% {BB*(1+5%)^2}
Amount paid
Remaining balance
2
$2,113.60
$2,330.24
$200.00
$2,130.24
4
$2,130.24
$2,348.60
$400.00
$1,948.60
The amount of principal paid in second payment
$181.6499
Therefore the amount of principal paid in second payment (at end of year 4) = Remaining balance at end of year 2 – remaining balance at end of year 4
= $2,130.24 -$1,948.60 = $181.64
Therefore correct answer is option $181.64
6. Duration calculation:
Therefore correct answer is option 3.61 years
7. Cost of liability is the price (Present value) of both zero coupon bonds
For first zero coupon bond
Bond price P1 = M / (1+i) ^n
Where,
Price of the bond P1 =?
Maturity value of the bond = $1,000
i = yield to maturity or priced to yield =10% per year
And time period for maturity n =1 year
Therefore
P1 = $1,000 / (1+10%) ^1
P1 = $909.09
For second zero coupon bonds
Bond price P2 = M / (1+i) ^n
Where,
Price of the bond P2 =?
Maturity value of the bond = $2,000
i = yield to maturity or priced to yield =12% per year
And time period for maturity n =2 year
Therefore
P2 = $2,000 / (1+12%) ^2
P2 = $1594.39
Therefore Cost of liabilities = P1+P2
=$909.09 +$1594.39
= $2503.47 or $2503
Therefore correct answer is option $2503
Year (t)
Amount (A)
PV = (A/(1+5%)^t
2
$200
$181.41
4
$400
$329.08
6
$600
$447.73
8
$800
$541.47
10
$1,000
$613.91
Total Loan (sum of Pvs)
$2,113.60
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.